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 Depdendent Variable

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 Dependent Variable

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# Polynomial Expressions

A polynomial is an expression which involves various powers of a variable. Some examples are:
and 5. The general form for a polynomial is:

Here the coefficients (a's) can be any real number. The number n, which is an integer, is known as the degree of the polynomial.

EX. is a polynomial of degree 3, with leading coefficient 5, and constant term -2.
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## Classifying Polynomials

Polynomials can be classified based on the degree (largest power), or based on the number of terms.

1 term = monomial
2 terms = binomial
3 terms = trinomial
and so on…

EX. is a binomial of degree 5.

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## Basic Operations on Polynomials

Just like with numbers, we often want to add, subtract, multiply and divide polynomials.

Adding polynomials is simply collecting like terms

EX.

Subtraction:

To subtract two polynomials, you simply use the distributive law, then collect like terms.

EX.

Notice you distribute the minus sign.

Multiplication:

While adding and subtracting were fairly easy, multiply two polynomials can quickly become a headache. To multiply you must repeatedly apply the distributive law, then collect like terms.

EX.

Notice that the distributive law was applied four times to complete that single multiplication

Division:
Division will be covered when we go into Rational Expressions. Notice that if you add, subtract, or multiply two polynomials, you end up with a polynomial again. This is not always true for division, and this is the reason we postpone this topic.
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## FOIL

There is a special case for multiplying polynomials, which occurs when you multiply a binomial times a binomial. In this case it is easier to use FOIL.

EX.